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At least 613 records · Page 34

Optimal control and controller location for distributed parameter elastic systems

A class of systems governed by second order partial differential equations and driven by controllers located at points r sub i, i = 1, ..., k, is considered. A cost functional quadratic in the time derivative of the state and the control is associated with the system. The optimal controller locations are defined as the ones which minimize the maximum of the cost over all possible initial states. An analytical solution to the associated Riccati equation is presented providing a convenient expression for determining the optimal locations.

Hamidi, M.↗

Theory of the optimally coupled Q-switched laser

The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.

Degnan, John J.↗

A method for generating numerical pilot opinion ratings using the optimal pilot model

A method for generating numerical pilot opinion ratings using the optimal pilot model is introduced. The method is contained in a rating hypothesis which states that the numerical rating which a human pilot assigns to a specific vehicle and task can be directly related to the numerical value of the index of performance resulting from the optimal pilot modeling procedure as applied to that vehicle and task. The hypothesis is tested using the data from four piloted simulations. The results indicate that the hypothesis is reasonable, but that the predictive capability of the method is a strong function of the accuracy of the pilot model itself. This accuracy is, in turn, dependent upon the parameters which define the optimal modeling problem. A procedure for specifying the parameters for the optimal pilot model in the absence of experimental data is suggested.

Hess, R. A.↗

Sensitivity of optimum solutions to problem parameters

Derivation of the sensitivity equations that yield the sensitivity derivatives directly, which avoids the costly and inaccurate perturb-and-reoptimize approach, is discussed and solvability of the equations is examined. The equations apply to optimum solutions obtained by direct search methods as well as those generated by procedures of the sequential unconstrained minimization technique class. Applications are discussed for the use of the sensitivity derivatives in extrapolation of the optimal objective function and design variable values for incremented parameters, optimization with multiple objectives, and decomposition of large optimization problems.

Sobieszczanski-Sobieski, J.↗

Maximum life spiral bevel reduction design

Optimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ratio under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed backcone distance of the spiral bevel gear set for a specified speed reduction, shaft angle, input torque, and power. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives.

Savage, M.↗

Estimation of optimal Kalman filter gain from non-optimal filter residuals

This paper presents a novel method of estimating the optimal steady state Kalman filter gain of a linear discrete time-invariant system from a non-optimal Kalman filter residual sequence. The relation between the optimal residual sequence and a signal derived from the non-optimal residual sequence is described by a Moving Average (MA) model whose coefficients are expressed in terms of the state space parameters and the optimal steady state Kalman filter gain. In order to identify the MA model, a whitening filter of the derived signal, which corresponds to an AutoRegressive (AR) model of the signal, is first identified using the least-squares method. Then the inverse filter of the whitening filter, which corresponds to the MA model, is calculated. From the coefficients of the identified MA model, the optimal steady state Kalman filter gain can be obtained. Numerical example is provided to illustrate the feasibility of this approach.

Chen, Chung-Wen↗

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Bernstein, Dennis S.↗

Asymptotic continuation method for trajectory optimization

A continuation method is applied to a singular perturbation parameter to obtain a new numerical method for computing optimal trajectories. This method allows one to use simply calculated reduced order approximations as starting solutions and continue the perturbation parameter until the optimal full-order solution is obtained. The method does not require the calculation of higher order correction terms nor does it require the perturbation parameter to be small - thus, it has potentially superior convergence properties compared to conventional asymptotic expansions when the perturbation parameter is large. A simple trajectory optimization problem is considered to illustrate the method.

Washburn, R. B., Jr.↗

3D Scanning System to Assess Gravity-Dependent Body Shape Changes

The human body shows unique morphological changes when exposed to different gravity conditions, including muscle atrophy, fluid shift, and spinal elongation. Such changes need to be incorporated for human-system integration in the vehicle habitat, garment, and spacesuit designs, as inaccurate body measurements can result in suboptimal crew protection that can potentially decrease injury tolerance. However, measurement tools have not been available for accurate assessments of body shape changes. This work aimed to develop a prototype 3-D body scanning system with the configuration and performance optimized for in-flight crewmember body scanning. A scan hardware system was developed using Intel RealSense commercial off-the-shelf 3D sensors. The sensor parameters were iteratively optimized and tested to obtain the performance level needed for body scanning. A scan booth structure was fabricated, with the overall size 4 x 4 x 8 feet. The specific number of sensors and mounting positions were determined by iterative simulations, which indicated that 16 cameras can capture 94% and 96% of body surface area from the 1st percentile female and 99th percentile male crew population subject. The mounted sensors were linked through a mix of USB-C and USB-3 cables and operated for data acquisition from a Linux laptop computer. A software prototype was developed using Python and Tkinter graphical user interface toolkit. A calibration procedure was also built using a panel of QR codes. A computer vision tool detected and decoded the unique ID and pattern locations of the QR codes. The calibration information determined the position and orientation of the 3D sensors with respect to each other. The scanner performance was assessed using a set of 3D printed custom manikins. The manikin size and shape were derived from the previous ISS study, which measured the crewmembers’ anthropometry changes across the different flight phases. The average anthropometric measurements at the pre-flight and flight day 15 were sampled and projected onto the 1st percentile female and 99th percentile male body shapes. Another pair of manikins were also 3D printed to simulate the neutral body posture, estimated from ISS microgravity environments. A preliminary analysis assessed the performance of the newly developed scanner against the reference scanner, which has been used at the NASA JSC for crew and test subject anthropometry. Although the new scanner data showed several artifacts and missing geometries in the occluded body areas such as armpits and crotch, overall shape matched with the reference scan. When the manikin surface coordinates were compared, a root mean square error of 1.3 cm was observed from the manikin torso segment. Linear measurements including the stature, knee height and circumference measurements at the chest and calf showed differences from the reference scan measurements, ranging between 0.3 and 0.9 cm. Overall, this work demonstrated a development framework for an in-flight scanner with design and operation optimized for crewmember body scanning. Further improvement can potentially provide previously unavailable anthropometric data from different gravitational environments, including 0-g, 1/6-g, and 1-g. Such data can improve suit fit, habitat design, exercise efficacy quantification and sizing of orthostatic intolerance garments.

K H Kim↗

Energetic Neutral Atom Imaging at Low Altitudes from the Swedish Microsatellite Astrid: Extraction of the Equatorial Ion Distribution

Energetic neutral atom (ENA) images obtained by the ENA imager on- board the Astrid satellite in the polar cap at 1000 km during a moderate magnetic storm (Dst greater than or equal to 80 nT) on 8 February 1995 are simulated using a parameterized model of the equatorial ion distribution and a six-component Chamberlain exo-sphere with parameters from the MSISE-90 model. By changing the ion parameters until a matching ENA image is obtained one can extract the equatorial ion distribution. Four consecutive images from different view points several of minutes apart are simulated assuming H(+) and O(+), respectively, as parent ions. The optimal set of parameters is extracted by minimizing the chi(exp 2) difference between simulated and observed ENA image using Powell's minimization algorithm. The optimal equatorial model ion distribution consists of O(+) peaked in around dusk. The lower intensity of fluxes obtained from vantage points closer to the pole is an effect of the loss cone of the parent ion distribution being empty.

Brandt, Pontus C:son↗

Chandrasekhar equations and computational algorithms for distributed parameter systems

The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas.

Burns, J. A.↗

Finite Element Analysis of MEMS Devices

A side-slide actuator and a corrugated diaphragm actuator will be analyzed and optimized this summer. Coupled electrostatic and fluid analyses will also be initiated. Both the side-slide actuator and the corrugated diaphragm actuator will be used to regulate the flow of fuel in a jet engine. Many of the side-slide actuators will be placed on top of a fuel injector that is still in the developmental stage as well. The corrugated diaphragm actuator will also be used to regulate the flow of fuel in fuel injectors. A comparative analysis of the performance matrix of both actuators will be conducted. The side-slide actuator uses the concept of mechanical advantage to regulate the flow of fuel using electrostatic forces. It is made from Nickel, Silicon Carbide, and thin layers of Oxide. The slider will have a hole in the middle that will allow fuel to pass through the hole underneath it. The goal is to regulate the flow of fuel through the inlet. This means that the actuator needs to be designed so that when a voltage is applied to the push rod, the slider will deflect in the x-direction and be able to completely block the inlet and no fuel can pass through. Different voltage levels will be tested. The parameters that are being optimized are the thickness of the diaphragm, what kind of corrugation the diaphragm should have, the length, width, and thickness of the push rod, and what design should be used to return the slider. The current possibilities for a return rod are a built in spring on the slider, a return rod that acts like a spring, or a return rod that is identical to the push rod. The final actuator design should have a push rod that has rotational motion and no translation motion, a push rod thickness that prevents warping due to the slider, and a large ratio of the displacement on the bottom of the push rod to displacement on the top of the push rod. The corrugated diaphragm actuator was optimized last winter and this summer will be spent completing the optimization of the coupled electrostatic and fluid flow parameters. It was found that Nickel is the best material to use for the diaphragm because it has a higher yield strength and allows for a larger stress, deflection and applied pressure. The parameters that were optimized were the wavelength and thickness of the diaphragm.

Corrigan, Jennifer↗

Theoretical and experimental analysis of injection seeding a Q-switched alexandrite laser

Injection seeding is a method for achieving linewidths of less than 500 MHz in the output of broadband, tunable, solid state lasers. Dye lasers, CW and pulsed diode lasers, and other solid state lasers have been used as injection seeders. By optimizing the fundamental laser parameters of pump energy, Q-switched pulse build-up time, injection seed power and mode matching, one can achieve significant improvements in the spectral purity of the Q-switched output. These parameters are incorporated into a simple model for analyzing spectral purity and pulse build-up processes in a Q-switched, injection-seeded laser. Experiments to optimize the relevant parameters of an alexandrite laser show good agreement.

Prasad, C. R.↗

Computerized optimal control system design for reusable and expendable boost vehicles.

An optimization technique has been developed which combines the practical features of hybrid simulation of the dynamic system under study with the systematic approach of modern control theory where a mathematically formulated design criterion is optimized by functional minimization. Standard hybrid computer optimization methods using high-speed repetitive simulations and gradient minimization schemes have been extended to obtain time-varying optimal gain schedules and reduce the sensitivity of the optimized system to parameter and disturbance uncertainties. In this approach the performance index is expressed in meaningful engineering terms that reflect the interactions among all major disciplines, structures, control/actuation system design, aerodynamics and performance. The basic optimization technique is developed and its application to current aerospace control problems including the space shuttle is presented in detail. In the discussion of the application, the controllers resulting from the technique are compared with controllers developed by conventional methods. The paper concludes with a review of the advantages and disadvantages of the technique and plans for future applications.

Connor, C. L.↗

Transient Growth Analysis of Compressible Boundary Layers with Parabolized Stability Equations

The linear form of parabolized linear stability equations (PSE) is used in a variational approach to extend the previous body of results for the optimal, non-modal disturbance growth in boundary layer flows. This methodology includes the non-parallel effects associated with the spatial development of boundary layer flows. As noted in literature, the optimal initial disturbances correspond to steady counter-rotating stream-wise vortices, which subsequently lead to the formation of stream-wise-elongated structures, i.e., streaks, via a lift-up effect. The parameter space for optimal growth is extended to the hypersonic Mach number regime without any high enthalpy effects, and the effect of wall cooling is studied with particular emphasis on the role of the initial disturbance location and the value of the span-wise wavenumber that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary layer equations, mean flow solutions based on the full Navier-Stokes (NS) equations are used in select cases to help account for the viscous-inviscid interaction near the leading edge of the plate and also for the weak shock wave emanating from that region. These differences in the base flow lead to an increasing reduction with Mach number in the magnitude of optimal growth relative to the predictions based on self-similar mean-flow approximation. Finally, the maximum optimal energy gain for the favorable pressure gradient boundary layer near a planar stagnation point is found to be substantially weaker than that in a zero pressure gradient Blasius boundary layer.

Compressible boundary layer↗

Effects of hand soldering MIL-PRF 55365 tantalum capacitors

Different values of MIL-PRF-55365 tantalum capacitors were subjected to three different types of soldering conditions— Convection Reflow, JPL Standard Hand Soldering, and Optimized Hand Soldering. The electrical parameters for a large number of capacitors of each value were measured before and after thermal soldering stress. The results indicate that tantalum capacitors subjected to convection reflow conditions experience detectable changes in electrical parameters; capacitors subjected to hand solder conditions show reduced changes in electrical parameters when compared to the reflow samples. Optimized hand solder conditions are shown to have a minimal effect on electrical parameters.

Sheldon, Douglas↗

Modal analysis and control of flexible manipulator arms

The possibility of modeling and controlling flexible manipulator arms was examined. A modal approach was used for obtaining the mathematical model and control techniques. The arm model was represented mathematically by a state space description defined in terms of joint angles and mode amplitudes obtained from truncation on the distributed systems, and included the motion of a two link two joint arm. Three basic techniques were used for controlling the system: pole allocation with gains obtained from the rigid system with interjoint feedbacks, Simon-Mitter algorithm for pole allocation, and sensitivity analysis with respect to parameter variations. An improvement in arm bandwidth was obtained. Optimization of some geometric parameters was undertaken to maximize bandwidth for various payload sizes and programmed tasks. The controlled system is examined under constant gains and using the nonlinear model for simulations following a time varying state trajectory.

Neto, O. M.↗